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Lesson 6.1 Notes: Comparing and Ordering Integers Warm-Up: We will be studying positive and negative numbers in this chapter. Answer these questions to see what you know. 1) If the temperature outside was negative, what would that tell you about the weather? 2) If the temperature outside was positive, what would that tell you about the weather? 3) If your bank account had a positive amount in it, what would that mean? 4) If your bank account had a negative amount in it, what would that mean? 5) List any words that you can think of that might tell you if a number was positive or negative: Positive Words Negative Words Stop___________________________________________ VOCABULARY: Integers Negative integers Positive integers Opposite Absolute Value Increase Decrease Deposit Withdrawal Integers and Their Opposites Zero Negative integer Positive integer Two numbers are opposites if they are the same distance from zero on a number line but are on opposite sides of zero. Examples: EXAMPLE 1 : Writing integers to represent real life situations Temperatures The temperature increased 12 degrees between 7 A.M. and 7 P.M. The temperature decreased 14 degrees between 7 P.M. and 7 A.M. You can use integers to represent the increase and decrease in the temperature: 12 degree increase: ____________ 14 degree decrease: ____________ NOW YOU TRY IT! 1) Write the opposite of each of the following integers: -17 _____ 41 _____ 3 _____ -215 _____ 2) Write each of the following as an integer: a) A decrease of 20 degrees _____ b) A deposit of $5 to your account _____ c) A withdrawal of $2 to your account _____ d) An increase of 3 degrees to the temperature _____ EXAMPLE 2: Comparing Integers Using a Number Line As you move RIGHT on the number line, numbers get LARGER or INCREASES. As you move LEFT on the number line, numbers get SMALLER or DECREASES. Let’s draw an example of this: a) Compare –1 and –4: Step 1: Graph -1 and -4 on the number line Draw a number line; number the intervals; put a point on the numbers you are graphing. Step 2: See which number is to the right and which is to the left. Answer: -1 ______-4 b) Compare –19 and -9: Answer: -19 ______-9 NOW YOU TRY IT! Graph and then complete the statement using < or > 3) 3 _____ –5 4) –7 ____ 2 5) –36_____ –20 EXAMPLE 3: Ordering Integers Using a Number Line Golf: The scores below are based on par for a 36 hole golf course. Golfer Score Patrick -3 Steven -6 Joe -2 Dan 1 Charles 2 Brad -4 Vincent -5 Randy 3 Graph each integer (score) on the number line (be sure to label it first!). 1. List the integers (scores) in order from least to greatest. 2. Which golfer has the highest score? 3. Which golfer has the lowest score? 4. Which golfer is in the lead? (hint: the goal in golf is to have a low score) EXAMPLE 4 - Finding Absolute Value Animals A seagull is flying at an altitude of 107 feet and a shark is swimming at a depth of –112 feet relative to sea level. Which animal is farther from sea level? Solution Seagull: | 107 | = The absolute value of a number n is written as | n |. Try: 1. | –6 | 2. | 5 | 3. |-105| Shark: | –112 | =